It is known to affix a so-called pressure accumulator in liquid-conducting conduits, to absorb and damp pressure variations and pressure surges in them, where this accumulator is connected with the conduit via a shunt line. This arrangement works well, as long as only one and the same liquid flows in the conduit. However, if a change in liquid occurs during operation, the residual amount of advancing liquid remaining in the shunt line and on the one side of the accumulator can prove to be disruptive. The residual liquid gradually mixes with the next liquid and contaminates the latter. This problem is particularly obvious in feed lines to application heads that carry fluid processing agents in the form of dye baths. Corresponding systems are known, for example, from German Patent A1 29 00 712 and German Patent A1 33 15 770 A1. If, for example, red dye was being used first, and a switch to yellow takes place, the residual amount of "dead" red dye remaining in the shunt line and on the one side of the accumulator will gradually mix with the yellow and turn it orange.